The story is told of a Chinese peasant invited to the emperor's palace to be rewarded for his loyal service. Would he rather be paid in gold or rice? Seeing the emperor at his chessboard, the peasant chooses rice, requesting one grain for the first square, two for the second, four for the third, and so on. Laughing at the man's stupidity, the emperor agrees but is bankrupted by the 64th square as the multiplying reward now totals more than all the rice in China.

Billions of billions – how can one begin to imagine such numbers, in grains of rice or anything else? Mark Wallinger does not flinch from the task. Each work in this marvellous new show attempts to number the numberless, to make visible some unimaginably vast concept all the way from infinity to eternity: and each work makes a piercing metaphor, often humorous, out of failure.

Stretching out before the visitor to the Baltic is an immense checkerboard floor: 65,536 chessboards, to be precise, laid edge to edge. On each square of each board lies a solitary pebble. Grey, cream, the size of a pawn or perhaps a queen, each stone has some visual affinity with the chess set but each is naturally unique; and the same suddenly seems true of each square. No longer just a black or white box, each square becomes a little kingdom for the pebble it contains; and each pebble acquires its own status by the same token. Everything is made to count, separately and together.

The effect from floor level is generalised, a grey miasma stretching into the distance. But from the viewing gallery above, every square has its special graphic distinction. Mathematics is clearly central to the work – from the simple binary opposition of chessboards to the super-perfect numbers involved – but there is a beautiful order in the spectacle itself: the sheer dizzying quantity of it all held in check, piece by piece, a beach contained in a chessboard.

Just beyond, not incidentally, is the sea itself, twinkling and lapping in Wallinger's new film Construction Site, receiving its UK premiere.

Three workmen are building a scaffolding tower on the shingle, a comic proposition in itself. A pole appears from the right, followed ages later by the builder carrying it. A speedboat breezes through as if to mock this slow and Sisyphean labour. There are mishaps and forgotten buckets, and a seagull bursts into the picture just as an ideal symmetry of structure is achieved. Every moment is surprising, a series of sight gags sustained over more than an hour in a masterpiece of comic timing.

This structure looks like a gigantic drawing, or a freestanding frame. It is eventually in such exact alignment with the sea's horizon that the workmen on the top appear to be walking on water. This is not a cinematic trick – transparency is crucial to everything Wallinger makes – just a simple coincidence of different perspectives.

Space swithers between two and three dimensions, the men seem variously giants or midgets, the sea appears flat as a picture; and time becomes mysterious too. No sooner have they finished than the workmen return to dismantle the structure – unless, perhaps, it was the other way round? A palindrome emerges and repeats itself continually, like the tides, transforming boats and buckets into running gags forever.

Construction Site is a most original combination of contemplation piece and absurdist comedy. Every pun – verbal and visual – is deeply intended. Puns, palindromes, mirror images, anagrams and inversions: these are all pivotal to Wallinger's art, succinct devices for multiplying the nuances of meaning.

His work can be extraordinarily condensed, as in the colossal letter "I" adorning the outside of the Baltic on a banner. The simplest expression of the self, I says everything and nothing, describes everyone and no one. It amounts to a universal self-portrait (one sign fits all) while paradoxically denying the possibility of summing oneself up in an image or a word.

Inside, at the opposite extreme, a slideshow is flashing up photographs of the several thousand marks Wallinger has chalked on brick walls all over London in the past few years. "Mark", says the mark, speaking of its maker as well as itself, sending up the narcissism of tagging as well as the futility of trying to leave one's mark upon London. It is the pun simultaneously multiplied and reduced to the absurd.

It would be hard to overstate the subtlety of these two meditations on self-centredness, each stimulating new thoughts long after one leaves the gallery and both achieved with the simplest possible means. No sleight of hand; the separate elements of Wallinger's works are always exposed, one feels, as a matter of principle. That principle may be moral, aesthetic or intellectual but it is generally all three, as in the most powerful piece in this show.

Just outside the central gallery is a vertiginous stairwell that drops 13 landings, a plunge so abrupt you lose all sense of orientation. With the simple addition of a couple of mirrors, one above and one below, Wallinger extends this continuum to infinity. The bottomless hell below reflects the eternal heaven above, on and on in both directions. Which way is up? The viewer stares into this illusion, entirely aware of the mechanics, but overpowered by its vision of an endless fall and the impossible ascent to heaven.

On either side two films are screening – an eye slowly blinking, a match gradually burning: pause, think, you might prevent disaster in a blink – and on the wall between them is Ono's famous Vietnam poster. "War Is Over" declares the faded headline; "If You Want It" whispers the tiny subtext. Hers may be a voice of perennial hope, but it is not without qualification.

This show breathes the true air of the 60s. It includes the early films of John and Yoko kissing, John breaking into an infectious slo-mo smile, Yoko suffering the clothes to be snipped from her body by strangers in Cut Piece. It has the glass labyrinth in which the wanderer becomes effectively blind and unable to find the way to the dark box at the centre, its hidden message as condensed as a haiku.

With its delicate calligraphy, translucent screens and fragile objects ceremonially presented on plinths, Ono's aesthetic appears strikingly Japanese. But her meanings are, of course, devoutly universal. For some, this will come across as sentimentality, as in her invitation to the public to smile on screen or leave a wish on a tree. But her sincerity is not in doubt.

Ono's gift is for the epigrammatic object or image; the blood-stained letter, the folded coat hanger doubling as forceps (death or birth), her footprints in step with John Lennon's on a sheet of paper, an overwhelming testimony of loss.

But most affecting of all is the remake of Cut Piece from 2003, when Ono was 70. The audience's reverence and obsession are now as much part of the performance as the artist's endurance. With every snip, they get closer to her fame while she remains resolutely dignified. The performance has turned into a life story.